The South African international struck with his first touch of the game after being brought off the bench by Simon Grayson.
It ensured Leeds gained deserved reward from a pulsating afternoon’s entertainment for the 31,601 crowd.
Norwich, buoyed by levelling the game in stoppage time at the end of the first half, started strongly in the second half.
Kasper Schmiechel had to be alert to turn a Wes Hoolahan round the post before Grant Holt struck a post after being found by Aaron Wilbraham.
The goal the Canaries craved came on 68 minutes when Hoolahan was played clear by Andrew Crofts and finished with aplomb.
To their credit, Leeds refused to panic and drew level just seven minutes later through a stunning volley from Somma.
It was no more the home side deserved on the balance of chances with Jonny Howson having earlier had a shot deflected just behind by Zac Whitbread.
Robert Snodgrass had also been guilty of wasting a three-on-two opportunity by delaying the final pass with Becchio and Howson free.
Once level, both sides continued to try and find the winner with only a last-gasp clearing head by Zac Whitbread preventing Somma from converting a sublime cross from Bradley Johnson.
Then, in the third and final minute of stoppage time, Billy Paynter was denied by a superb save by John Ruddy.
Somma has been an unused substitute eight times this season and Grayson said: “He’s a great lad. He’s never once complained, he understood when I left him out last weekend, he understood today.
“He’s got a fantastic attitude, he works ever so hard and is a massive team player and I wouldn’t say he’s best coming off the bench because he scores for us when he starts as well.
“He appreciates what we’ve done for him in terms of bringing him to this football club, of what he can be and what we’ve made him.
“But he’s a great lad to work with and I’m sure he’ll only get better.
“I don’t know his goals ratio to minutes he’s spent on the pitch, but it can’t be far away from a goal a game now.
“That’s a fantastic effort for him. He went to Lincoln last season and got a lot of goals there too and that’s why he signed a long-term contract for us earlier this season.”